Robust exponential attractors for a class of non-autonomous semi-linear second-order evolution equation with memory and critical nonlinearity |
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| Authors: | Fang-hong Zhang Shan-lin Wang Li Wang |
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| Institution: | 1. Regional Circular Economy key Laboratory of Gansu Higher Institutions , Lanzhou, China.;2. Department of Economics and Trade, Longqiao College of Lanzhou University of Finance and Economics , Lanzhou, China.zhangfanghong2010@126.com;4. Department of Economics and Trade, Longqiao College of Lanzhou University of Finance and Economics , Lanzhou, China. |
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| Abstract: | In this article, we investigate a class of non-autonomous semi-linear second-order evolution with memory terms, expressed by the convolution integrals, which account for the past history of one or more variables. First, the asymptotic regularity of solutions is proved, while the nonlinearity is critical and the time-dependent external forcing term is assumed to be only translation-bounded (instead of translation-compact), and then the existence of compact uniform attractors together with its structure and regularity is established. Finally, the existence of robust family of exponential attractors is constructed. |
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| Keywords: | Nonautonomous semi-linear second-order evolution asymptotic regularity uniform attractors robust exponential attractors critical exponent |
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